Optimization of the Subspace Iteration Method for the Lambda Modes Determination of a Nuclear Power Reactor

In this paper, we propose different alternative approaches to optimize the subspace iteration method which obtains the dominant λ-modes of a nuclear power reactor. We present a variational acceleration for the iterative process, a coarse grain parallelizatization approach, and a multistep algorithm to choose efficient initial estimations for the subspace iteration method. We have tested the efficiency of the developed algorithms with a 3D realistic problem, corresponding to a static configuration of the reactor Ringhals I.     

求解间断边值问题的重心插值单元配点法

按照间断边值问题的连续区间划分计算单元,在每一个单元上采用重心Lagrange插值近似未知函数,得到每一个单元上的微分矩阵。利用微分矩阵离散微分算子,得到每一个单元上微分方程的离散代数方程组,组装得到边值问题求解的整体代数方程组。将边界条件和单元间的连续性条件,利用微分矩阵离散为代数方程,采用置换法施加边界条件和单元间的连续性条件,得到修正的代数方程组,求解代数方程组得到节点处的函数值。二阶和三阶间断边值问题的数值算例验证了本文方法的有效性和计算精度。     

基于预测误差扩展的可逆文本水印算法

为了避免在水印嵌入后造成文本内容的永久性改变,该文借鉴图像中可恢复水印的思想,将预测误差扩展应用于文本文档,提出了一种基于预测误差扩展的可逆中文文本水印算法。该算法以句子为单位,通过上下文搭配度大小选择可替换的词语,最后利用预测误差扩展和混沌序列,实现水印的嵌入。研究结果表明该算法不仅具有较高的安全性,而且能有效地提取水印和无损地恢复出原始文本。     

基于多知识源的语义搭配知识获取及表示方法

为更全面准确地从字词搭配中获取语义搭配信息,提出一种新的语义搭配知识提取模型和知识库的表示方法.利用特殊度度量词语搭配的相关程度,在此基础上,基于知网的语义信息,实现从42万条记录的词语搭配中定量地抽取语义搭配信息.实验结果表明,该方法的语义搭配准确率为92.1％,且较大地扩充了字词搭配的规模.     

亚油酸乳状液体系氧化模型与求解

研究了恒表面氧压静置式无限氧补偿条件下乳状液中亚油酸的氧化,通过综合考虑气液边界传质阻力、水相扩散、油水边界乳化剂膜边界层阻力、多不饱和脂肪酸(PUFA)自催化氧化反应动力学,建立了扩散-氧化数学模型。采用非对称正交配置法处理特殊边界,求解偏微分方程组,计算了氧化过程中乳状液中氧和亚油酸在垂直于液膜方向的浓度分布,计算方法快捷、有效;结合数学模拟试验和实验值,确定了气液界面氧的液膜传质系数和水相中氧的扩散系数。实验验证该模型能较好地拟合静置式无限氧补偿条件下乳状液中氧的扩散和亚油酸的氧化过程。     

Thermo-bioconvection effect on hybrid nanofluid flow over a stretching/shrinking melting wedge

The research focused on nanomaterial solutions and their flow characteristics in relation to their usage. The application of such composites in biological rheological models, in particular, has received a lot of interest. The use of nanofluids in cooling tiny electronic devices like microchips and associated devices cannot be emphasized. Our goal is to explore the influence of a binary chemical reaction and Arrhenius activation energy on a hybrid nanofluid over a melting wedge in a spongy media. It is anticipated that the water-based nanoparticle contains gyrotactic microbes. By using appropriate similarity variables, the resultant dimensional nonlinear boundary-layer model is reduced and turned into a dimensionless form. A Chebyshev spectral collocation approach is useful in solving the highly nonlinear model. In terms of physical importance, the effects of important factors on developing profiles are displayed graphically and explained. Computational outcomes are obtained via MATHEMATICA. The plot of residual error is also shown to demonstrate the method's rapid convergence. According to the study's findings, by increasing the melting parameter, the rate of heat transportation at the wall decreases greatly on the average of 12.81%, but the Sherwood number becomes effective for the chemical reaction rate with a rate of about 24.81%.     

Multi-fidelity design optimization of solid oxide fuel cells using a Bayesian feature enhanced stochastic collocation

We develop a multi-fidelity surrogate modelling approach to replace the complex and costly physics-based computer models that are often used in the optimization of solid oxide fuel cell (SOFC) performance, or the simplified models that are used in lieu of complex models. We extend multi-fidelity stochastic collocation through a feature engineering step, and eliminate the requirement for the exact low-fidelity output at the inference stage. In contrast to previous approaches, the surrogate model we develop provides detailed spatial information, rather than one or more scalar outputs. This allows for the incorporation of such information into the objective of the optimization study, with the flexibility to choose from more than one objective, such as a minimum, maximum or average. Furthermore, the detailed spatial information can be used for general design purposes, such as ensuring uniformity in reactant and potential distributions. From the results on a 3-d SOFC model, we demonstrate highly accurate predictions of multiple spatially distributed quantities at up to spatial 250,000 locations. The results are superior to state-of-the-art multi-fidelity approaches, particularly for low numbers of high fidelity training points. We use the surrogate model to optimize the SOFC performance with respect to different objectives (including with nonlinear constraints and multiple objectives), with results that are accurate and are obtained in a fraction of the time required for the full model.     

Sparse Grid Collocation Method for an Optimal Control Problem Involving a Stochastic Partial Differential Equation with Random Inputs

In this article, we propose and analyse a sparse grid collocation method to solve an optimal control problem involving an elliptic partial differential equation with random coefficients and forcing terms. The input data are assumed to be dependent on a finite number of random variables. We prove that an optimal solution exists, and derive an optimality system. A Galerkin approximation in physical space and a sparse grid collocation in the probability space is used. Error estimates for a fully discrete solution using an appropriate norm are provided, and we analyse the computational efficiency. Computational evidence complements the present theory, to show the effectiveness of our stochastic collocation method.     

Fractional optimal control problems with both integer-order and Atangana–Baleanu Caputo derivatives

This article considers fractional optimal control problems (FOCPs) including both integer-order and Atangana–Baleanu Caputo derivatives. First, the existence and uniqueness of the solution of a fractional Cauchy problem is given. Then, applying calculus of variations and Lagrange multiplier method, we present necessary optimality conditions of FOCPs and sufficient optimality conditions are also given under some assumptions. Next, a collection method is developed to derive numerical solutions by using shifted Legendre polynomials. Finally, error estimate of numerical solutions is also provided, and numerical examples further show the accuracy and feasibility of our method.